\xiti

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\begin{xiaotis}

\xiaoti{下列各题中的两个项，是不是同类项？}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={18em, colsep=0pt}}
        \xxt{$\dfrac{1}{3}x^2y$ 与 $-3x^2y$；}  & \xxt{$0.2a^2b$ 与 $0.2ab^2$；} \\
        \xxt{$11abc$ 与 $9ab$；}                & \xxt{$3m^2n^3$ 与 $-n^3m^2$；} \\
        \xxt{$5xy$ 与 $25yx$；}                 & \xxt{$4xy^2z$ 与 $4x^2yz$；} \\
        \xxt{$125$ 与 $-4\dfrac{1}{8}$；}       & \xxt{$6^2$ 与 $x^2$。}
    \end{tblr}

\end{xiaoxiaotis}


\xiaoti{合并下列各式中的同类项：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={18em, colsep=0pt}}
        \xxt{$15x + 4x - 10x$；} & \xxt{$-6ab - ab + 8ab$；} \\
        \xxt{$-p^2 - p^2 - p^2$；} & \xxt{$1\dfrac{2}{3} + \dfrac{5}{6} - \dfrac{1}{2}$；} \\
        \xxt{$\dfrac{1}{3}x^3 - \dfrac{5}{6}x^3 + \dfrac{1}{2}x^3$；} & \xxt{$-4a^2b + 5a + 5a^2b + 2a - 3$；} \\
        \xxt{$\dfrac{1}{4}x - 0.3y - \dfrac{1}{2}x + 0.3y$；} & \xxt{$m + m + m - n^2 - n^2$；} \\
        \xxt{$11x^2 + 4x + 1 - x^2 - 4x - 5$；} & \xxt{$5x^2 + 4 - 3x^2 - 5x + 6x^3 + 3x$。}
    \end{tblr}

\end{xiaoxiaotis}


\xiaoti{把 $(a + b)$、$(x - y)$ 各当作一个因式，合并下列各式中的同类项：}
\begin{xiaoxiaotis}

    \xxt{$4(a + b) + 2(a + b) - (a + b)$；}

    \xxt{$3(x - y)^2 - 7(x - y) + 8(x - y)^2 + 6(x - y)$。}

\end{xiaoxiaotis}


\xiaoti{先合并下列程式中的同类项，再求它们的值：}
\begin{xiaoxiaotis}

    \xxt{$3c^2 - 8c + 2c^3 - 13c^2 - 2c - 2c^3 + 3$，其中 $c = 4$；}

    \xxt{$3y^4 - 4x^3y - 4y^4 + 2x^3y$，其中 $x = -2$，$y = \dfrac{2}{3}$。}

\end{xiaoxiaotis}


\xiaoti{下面的去括号对不对？如果有错，把它改正：}
\begin{xiaoxiaotis}

    \xxt{$a^2 - (2a + b + c) = a^2 - 2a + b + c$；}

    \xxt{$a + (-3x + 2y - 1) = a - 3x + 2y - 1$；}

    \xxt{$(a + 1) - (-b + c) = a + 1 - b - c$；}

    \xxt{$-(2x - y) + (z - 1) = -2x - y + z - 1$。}

\end{xiaoxiaotis}


\xiaoti{化简：}
\begin{xiaoxiaotis}

    \xxt{$(2x - 3y) + (5x - 4y)$；}

    \xxt{$(8a - 7b) - (4a - 5b)$；}

    \xxt{$a - (2a + b) + 2(a - 2b)$；}

    \xxt{$3(5x - 4) - 2(3x + 5)$；}

    \xxt{$(8x - 3y) - [4x + (3y - z)] + 2z$；}

    \xxt{$-4x^2 + [5x - 8x^2 - (-13x^2 + 4x) + 2] - 1$；}

    \xxt{$2a - \{-3b + [4a - (3a - b)]\}$；}

    \xxt{$-[-(-a^2) - b^2] - [+(-b^2)]$。}

\end{xiaoxiaotis}


\xiaoti{在下列程式的括号里，填上适当的项：}
\begin{xiaoxiaotis}

    \xxt{$4x^2 - 3x + 6 = + \; \ewkh[6em]$；}

    \xxt{$4x^2 - 3x + 6 = - \; \ewkh[6em]$；}

    \xxt{$a^2 - ab - 3a + 3b = a^2 - ab + \ewkh[4em]$；}

    \xxt{$a^2 - ab - 3a + 3b = a^2 - ab - \ewkh[4em]$；}

    \xxt{$a^2 - b^2 - (b - a) = a^2 - b^2 + \ewkh[4em]$；}

    \xxt{$a^4 + (-a^2 + 2a - 1) = a^4 - \ewkh[5em]$。}

\end{xiaoxiaotis}


\xiaoti{在下列程式的括号里，填上适当的项：}
\begin{xiaoxiaotis}

    \xxt{$(a + b + c)(a - b - c) = [a + \ewkh[3em]] [a - \ewkh[3em]]$；}

    \xxt{$(a - b + c)(a + b - c) = [a - \ewkh[3em]] [a + \ewkh[3em]]$；}

    \xxt{$(-a + b + c)(a + b - c) = [b - \ewkh[3em]] [b + \ewkh[3em]]$；}

    \xxt{$(a + b - c -d)(a - b + c - d) = [(a - d) + \ewkh[3em]] [(a - d) - \ewkh[3em]]$。}

\end{xiaoxiaotis}


\xiaoti{按着下面的要求，在多项式
    $$m^4 - 2m^2n^2 - 2m^2 + 2n^2 + n^4$$
    里添上括号：把四次项结合起来，放在前面带有 “$+$” 号的括号里，
           同时把二次项结合起来，放在前面带有 “$-$” 号的括号里。
}

\end{xiaotis}
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